How Is the Resultant Force on a Car Calculated?

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SUMMARY

The resultant force exerted by a 1040 kg car pulling a 300 kg trailer, accelerating at 2.11 m/s², is calculated using Newton's second law (F = ma). The total mass of the system is 1340 kg, resulting in a resultant force of 10425 N. The direction of this force, determined through trigonometric calculations, is approximately 12.15 degrees from the vertical. The analysis includes a free body diagram to visualize the forces acting on the system.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Basic knowledge of free body diagrams
  • Familiarity with trigonometric functions (sine and cosine)
  • Concept of resultant force and its components
NEXT STEPS
  • Study the application of Newton's laws in multi-body systems
  • Learn about friction forces and their impact on acceleration
  • Explore advanced topics in dynamics, such as vector resolution
  • Investigate the effects of air drag and friction in real-world scenarios
USEFUL FOR

Students in physics, automotive engineers, and anyone interested in understanding the dynamics of vehicles and forces in motion.

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Homework Statement



A 1040 kg car is pulling a 300 kg trailer. Together the car and trailer move forward with an acceleration of 2.11 m/s2. Ignore any frictional force of air drag on the car and all frictional forces on the trailer. What is the resultant force exerted by the car on the road and in what direction (measured from the left of vertically downwards)?

Homework Equations



F = ma

The Attempt at a Solution



I already found the magnitude by making a free body diagram with the acceleration of the car going on the negative x axis, and the weight of the car on the negative y axis. then, i squared the values of the force in the y direction and x direction, added them together and took the square root of that, finding the force to be 10425. so now i tried doing the sin-1 of x component/y component and got theta to be 12.15 degrees.

i attached a paint version of my free body diagram. any help would be greatly appreciated.
 

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Recalculate the horizontal component (the friction force). Realize that the friction force must accelerate the entire system of both car and trailer.
 

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